The move comes after the planned deficit in the 2011-12 budget was revised down from 11% to 8.6% of GDP, Mr Radwan told Reuters news agency.
An adviser told AFP news agency the decision had been partly a response to the “pressure of public opinion”.
Many of those who took part in Egypt’s uprising denounced the role of the IMF.
It was seen as bolstering the rule of now-deposed President Hosni Mubarak while imposing harsh economic conditions that benefited the rich more than the poor, says the BBC’s Arab affairs editor Sebastian Usher.
But the uprising led to a haemorrhaging of public finances, he says.
But Mr Radwan turned to the IMF in May, telling the BBC that the situation was “very difficult”, and extra funds were needed to finance the demands of the people on the heels of the revolution.
He agreed a $3bn (£1.9bn) 12-month stand-by loan facility – an agreement which came on top of loan deals agreed with the World Bank and the African Development Bank.
Despite apparently lenient terms on which the IMF offered the loan, many Egyptians were unhappy, feeling it was a betrayal of the protest movement that had denounced the IMF as a tool of imperialism, our correspondent says.
Mr Radwan now says that following discussions with civic and business groups and the military council, the budget forecast has been revised down from a deficit of 170 billion Egyptian pounds ($28.5bn; £17.8bn) to 134 billion pounds, and loans are thus not needed at this stage.
Dilemma
He said Egypt would cover the greater part of the deficit from “local sources”, as well as packages from Gulf Arab states such as Saudi Arabia and Qatar, which he said had provided $500m in the past week as a “gift”.
The issue over the loan highlights the huge dilemma facing Egypt – and the rest of the Arab world, our correspondent says.
The protesters want a complete change from the lumbering, state-controlled economic systems that failed to provide jobs for tens of millions of young people.
But the unrest has paralysed business and decimated tourism. To remake Arab economies, many state jobs will have to go – and the private sector is too weak to provide replacement jobs